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The class of automaton groups is a rich source of the simplest examples ofinfinite Burnside groups. However, there are some classes of automata that donot contain such examples. For instance, all infinite Burnside automaton groupsin the literature are generated by non reversible Mealy automata and it wasrecently shown that 2-state invertible-reversible Mealy automata cannotgenerate infinite Burnside groups. Here we extend this result to connected3-state invertible-reversible Mealy automata, using new original techniques.The results provide the first uniform method to construct elements of infiniteorder in each infinite group in this class.

A connected 3-state reversible Mealy automaton cannot generate an infinite Burnside group